Energy Resolution Enhancement of Retarding Type Electron Analyzer for Photoelectron Thermometry

Transcription

1 SICE Journal of Control, Measurement, and System Integration, Vol. 6, No. 4, pp , July 2013 Energy Resolution Enhancement of Retarding Type Electron Analyzer for Photoelectron Thermometry Ikuo KINOSHITA and Juntaro ISHII Abstract : A novel retarding type electron energy analyzer implementing an electrostatic lens system to achieve a high energy resolution sufficient to measure thermodynamic temperature has been investigated based on the electron trajectory analysis. The energy resolution of the analyzer depends linearly on the retarding energy with a modulus of 0.05 %. The voltages to be applied to the electrodes in the analyzer are found to be controllable linearly against the retarding voltage. The analyzer has threshold energies, whose effect can be excluded in practical measurements. Key Words : temperature measurement, ultraviolet photoelectron spectroscopy, electron energy analyzer. 1. Introduction Thermodynamic temperature of atomic layer surface is very important in surface science and engineering. Each interaction between atom and surface in order of a few atomic layers appears at its own temperature, i.e., thermal energy state. In a measurement of temperature-programmed desorption the surface is heated in a controlled way and a mass spectrometer is used in ultra high vacuum (UHV) to measure the rate at which products desorb from the surface. Temperature is a critical parameter of a thermal energy of a reaction on the surface or a binding energy to the surface [1]. Scanning tunneling microscopy measurements have revealed self-assembled nanostructures of molecules on surfaces which change their configurations at different temperatures [2],[3]. Accurate and noncontact measurement and control of surface-local temperature in UHV is of increasing significance. In semiconductor engineering highly-integrated devices are processed with strict temperature control. It needs practical methods for measuring temperature of device surfaces in UHV. In surface science experiments two kinds of thermometers are commonly used to measure temperature of sample surfaces in UHV, thermo-couple and infrared radiation thermometer. Thermo-couple measures a contact voltage of two different metal wires, which make a contact with each other in a place where temperature is to be measured. Simple and easy to handle in UHV, but, unable to make non-contact measurement of fragile surfaces, a thermo-couple can be used as an indirect surface temperature sensor mounted into a sample holder. Infrared radiation thermometer measures thermal radiation emitted from a sample surface. Since it is unnecessary to make contact with sample surface, the thermometer measures the temperature through the UHV window. However, radiation thermom- Graduate School of Nanobioscience, Department of Nanosystem Science, Yokohama City University, 22-2 Seto, Kanazawa, Yokohama, Kanagawa , Japan National Metrology Institute of Japan, AIST Tsukuba Central Umezono, Tsukuba, Ibaraki , Japan (Ikuo Kinoshita) ikinoshi@yokohama-cu.ac.jp, (Juntaro Ishii) j-ishii@aist.go.jp (Received September 13, 2011) (Revised August 28, 2012) etry has also intrinsicdifficulties in practical applications. Prior information on optical property, i.e. emissivity, of the sample surface is essential in order to determine the true temperature of the surface. Furthermore, radiation thermometer signals are affected by optical condition surrounding the sample. Therefore, there is a real need for developing a new approach to measure thermodynamic temperature of atomic layer surface in non-contact and without in-process calibration. Electrons in valence bands of some metals act as a free fermion gas. The electron occupancy of states is governed by the Fermi-Dirac distribution. Accurately measured physical quantities concerned with electrons as fermions may be used as thermometric parameters to determine the fundamental temperature τ = k B T with the thermodynamic temperature T, and the Boltzmann constant k B. Photoelectron spectroscopy is a sophisticated tool to investigate the electronic states in solids [4], because the photoelectron spectrum reflects occupancy of electrons in energy states. The edge of the spectrum for some metal forms the Fermi-Dirac distribution with high fidelity. Thus, the photoelectron spectroscopy has a highly potential to be a new approach to thermodynamic temperature measurement, which we call photoelectron thermometry. In the authors previous work, feasibility of ultraviolet photoelectron spectroscopy (UPS) as a method to measure thermodynamic temperature was investigated [5]. The theoretical analysis was based on calculations of the sensitivity of the Fermi-Dirac distribution function to temperature variation and retrieved temperature shift on an assumption of the energy resolution of the photoelectron measurements. The feasibility of the photoelectron thermometry with temperature accuracy below 1 K was verified by an electron energy analyzer with high sensitivity and sufficient energy resolution better than 2 mev in the temperature range over 25 K. The authors also proposed a novel electron energy analyzer design to achieve sufficiently high sensitivity and energy resolution for a practical thermometry. In the proposal, the energy resolution was estimated in a restricted energy range from 4.0 ev to 4.4 ev of retarding energy to be scanned for a spectrum with a specific combination of photon energy and work function. In order to put the proposed electron energy analyzer into JCMSI 0004/13/ c 2011 SICE

2 SICE JCMSI, Vol. 6, No. 4, July practical applications, further detailed analysis of the electron trajectory in a wider range of electron kinetic energy is necessary. The detailed quantitative investigation by the electron trajectory simulation reveals its technical features, i.e. superiority and an applicable limit of the analyzer in practical conditions. In this paper, trajectories of electrons with various kinetic energies and emission angles for extended retarding energy region from 2 ev to 8 ev are computed for the novel electron energy analyzer. The trajectory simulation provides discrimination in electron counting and estimates the energy resolution. A set of simulations for four retarding energies in wider range clarifies the retarding energy dependence of energy resolution, which was not defined in the previous paper [5]. Furthermore, the simulation of electrons with high kinetic energy reveals the appearance of threshold energies and their effect to the measured photoelectron spectra. Methods to prevent photoelectron spectra from being distorted by the threshold energy are also discussed by classifying the characters of the threshold energies. 2. Design and Simulations Various types of electron energy analyzers are used as electron measurement methods [6]. The spherical deflector analyzer is mostly used in UPS. This type of analyzer can measure the photoelectron in an acceptance angle of ±1 and is used for angle-resolved UPS, which is desirable to study the electronic band structures of materials. However, this type of analyzer is improper for photoelectron thermometer because of its low sensitivity of electron counting with a small solid angle. The retarding grid analyzer is basically composed of two hemispherical grids and a spherical collector. The inner grid and a sample are grounded to make a field-free intervening region between them. The outer grid is based negative at V R (< 0) and retards the electrons with kinetic energies below the retarding energy E R = ev R. The collector is biased positive to collect all electrons that pass through the retarding grid. This type of analyzer detects electrons emitted in much wider angles and provides higher counting rates of electrons than the spherical deflector analyzer. This highly sensitive analyzer without an angle-resolved function has an advantage on measuring thermodynamic temperature by fitting the photoelectron energy spectrum to the Fermi-Dirac distribution function. On the other hand, the existing retarding grid analyzers have poor energy resolutions compared with the spherical deflector analyzers, because the electrodes of the analyzer consist of optically highly transparent grids. The electrostatic potential on the grid made of a metal mesh is actually inhomogeneous in space for electrons, especially for low energy electrons (< 10 ev). The energy resolution of the conventional type of retarding grid analyzer is worse than 100 mev for electrons of around 100 ev and is inadequate for practical photoelectron thermometry. The electron energy analyzer newly proposed in the present study adopts the basic configuration of the retarding grid analyzer remaining the advantage of high sensitivity. Schematic drawing was illustrated in Fig. 1. One remarkable feature of the analyzer is its distinctive structure of electrodes consisting of solid hemispherical electrodes with coaxial apertures instead of transparent mesh electrodes. A large number of axes of apertures are arranged radially from the sphere center of electrodes, at which photoelectrons emit. Difference of voltages applied to Fig. 1 Schematic drawing of the new electron energy analyzer with electrostatic lens system for photoelectron thermometry. the neighboring electrodes causes an electrostatic lens, einzel lens, between the apertures of the electrodes [7]. The combination of einzel lenses controls electrons to let the electrons go vertically into the aperture of the retarding electrode at the center of the aperture. Introducing the electrostatic lens system to the retarding type electron analyzer provides significant enhancement of the energy resolution of the analyzer. Simulations of electron trajectory in this study were performed by a computer software, SIMION 3D [8], which could calculate electric fields and the trajectories of charged particles in those fields when a configuration of electrodes with voltages and initial conditions of particles is given. The electrostatic potentials of positions outside of the electrodes are determined as a potential array in a volume by solving the boundary value problem s Laplace equation via the finite difference method. After a potential array is determined, ions (electrons) can be flown through its volume. In the present work, electron trajectories along an axis of apertures were calculated as a prime case because the whole assembly of electrodes in Fig. 1 is a bunch of identical electrode components. Six electrodes were set in a cylindrical symmetry with coaxial circular apertures as shown in Fig. 2. The size of apertures and the distance between the electrodes were all same. The acceptance angle was set ±0.9. A grounded enclosure between the electron emitter (sample) and first electrode makes a field-free intervening region. The second, third, forth electrodes were biased at voltages V 1, V 2 and V 3, respectively, and the fifth electrode as a retarding electrode was biased at V R. The last electrode as a detector was biased positive to pull out the electrons though out the retarding electrode. In this condition, four einzel lenses are established between the emitter and the detector. Electrons with various kinetic energies were emitted from the center of the emitter at the emission angles from 0 to 0.9 with a step of 0.1 from the central axis of the electrodes. Four values of retarding energy were selected as E R = ev, ev, ev, and ev. The retarding energies of ev and ev are almost worth to the kinetic energy of photoelectrons from Fermi level in assumptions with the work function of poly crystal Gold (5.4 ev) and photon energies of Xe I (9.57 ev) and Ar I (11.83 ev), respectively. The other two

3 240 SICE JCMSI, Vol. 6, No. 4, July 2013 Fig. 2 Configuration of electrodes for simulations and typical electron trajectories. retarding energies were set to investigate the dependence of energy resolution on the retarding energy. 3. Results and Discussions The voltage V 1 was roughly determined to let the electrons with the kinetic energy just above the retarding energy converge at a point just behind the electrode V 1 in the first stage. Then the voltages V 2 and V 3 were determined to let the electrons collimate before the retarding electrode. In the second stage, optimization was done to obtain the best energy resolution by changing the three parameters of voltage one by one and monitoring the electron trajectories. Schematic trajectories of electrons passing though the retarding electrode are displayed in Fig. 2. The first einzel lens between the first and second electrodes focuses the electron beam emitted with emission angles within ±0.9. The other three lenses collimate the electron beam at the center of the aperture of retarding electrode. Table 1 Voltages applied to electrodes. E R (ev) V R (V) V 1 (V) V 2 (V) V 3 (V) ± ± ± ± ± ± ± ± ± ± ± ±0.55 The optimized voltages applied to the electrodes are summed up in Table 1. It is found that the voltages V 1 and V 3 change linearly against the retarding voltage V R. V 2 is around 0 V, and thus 0 V can be substituted for the voltage V 2. These are important results of the present study in the point of turning the voltages of electrodes in a spectral measurement where the retarding voltage has to be scanned. In a conventional electrostatic lens system, the applied voltages to electrodes do not change linearly and a linear approximation to the complicated response is applied to control the system in practice [7]. The present resulting linear changes of these voltages are very use- Table 2 Results of simulation for E R = 2.000eV Table 3 Results of simulation for E R = 4.200eV Table 4 Results of simulation for E R = 6.400eV Table 5 Results of simulation for E R = 8.000eV ful and can make it possible to control the voltages of the electrodes precisely using conventional electronic devices without any approximations in order to achieve a higher energy resolution. The results of the simulations are displayed in Tables 2-5 for the retarding energy E R = ev, ev, ev, and ev, respectively. The open circle ( ) denotes the electron, which was repelled or collides to an electrode, not passing through the retarding electrode, and the filled circle ( ) denotes the electron passing through the retarding electrode and is captured by the electron detector. In all cases, the electrons with the kinetic energy not less than the retarding energy passed through the retarding electrode. The energy resolution in the retarding type analyzer is assessed by the effective range of cut-off in the kinetic energy of the electron passing through the retarding electrode at each E R.

4 SICE JCMSI, Vol. 6, No. 4, July In the case of E R = ev, the range of the cut-off energy against the emission angle was 1 mev. In the same way, each range of the cut-off energy for E R = ev, ev, and ev was 2 mev, 3 mev, and 4 mev, respectively. In a picture of the ideal retarding energy analyzer, all electrons with kinetic energies over the retarding energy are detected and counted. However, the simulations for much higher kinetic energies revealed the existence of the threshold energy. The threshold energy E th is the boundary kinetic energy, over which, even with a kinetic energy above the retarding energy, an electron does not pass the retarding electrode. In the present analyzer the combination of einzel lenses is set in the most effective way to collimate electrons with kinetic energies around the retarding energy. However, the lens system loses the function as a collimator for electrons with much higher kinetic energies than the retarding energy. In the present condition of electrodes all electrons at the emission angle from 0 to 0.4 with higher kinetic energies than E R passed through the retarding electrode. No threshold energy appeared. On the other hand, at the emission angle from 0.5 to 0.9 threshold energies appeared and the electrons with higher kinetic energies than E th were not collimated by the lens system and did not pass the retarding electrode. Table 6 shows threshold energies E th in ev. Further results of the simulations for all retarding energy of E R = 2.0, 4.2, 6.4, 8.0 evs ensured that threshold energies at the emission angles from 0.6 to 0.9 did not change against the slight variation within a few mv of the retarding voltage V R with the fixed lens voltages V 1, V 2,andV 3. This is because these electrons from 0.6 to 0.9 emission angles with kinetic energies more than E th collide to the electrodes in front of the retarding electrode and do not reach the aperture of the retarding electrode. On the other hand, the threshold energy at the emission angle of 0.5 changed when the retarding voltage varies up and down with the fixed lens voltages, since the electron with the threshold energy reaches the aperture of the retarding electrode. The former behavior of threshold energy against retarding energy is regarded as dc-components in count rate, and the latter is as ac-components. One might suspect that the appearance of threshold energy declined the energy resolution in the retarding type energy analyzer. However, with this type of analyzer the count rate as a function of retarding energy builds the integrated spectrum. The dc-component of the signal can be excluded in a differential mode of measurement using a lock-in amplifier to get the normal energy distribution spectrum. On the other hand, the threshold energy for the ac-component is far above the retarding energy as seen in the column of 0.5 emission angle in Table 6. An auxiliary grid as a pass filter might be used in front of the electron detector and biased to voltage lower and higher than the retarding voltage. Subtracting the count rate with the low bias from the count rate with the high bias makes the accomponent invalid. Therefore, the threshold energies do not Table 6 Thershold energies E th (ev). E R (ev) Emission angle ( ) Fig. 3 Energy resolutions versus retarding energies. degrade the energy resolution practically. The estimated energy resolution versus the retarding energy is summarized in Fig. 3. The energy resolution dependes linearly on the retarding energy and was found to be 0.05 % against the retarding energy. The linear dependence of the energy resolution is understandable in the course of linear changes of applied voltages. However, the value of 0.05 % is extremely small in comparison with ones of the conventional retardingtype electron energy analyzers [6]. The dependence of energy resolution on the retarding energy is undesirable feature, since the dependence makes different energy resolution at each kinetic energy in a spectrum. However, in a determination of thermodynamic temperature based on the Fermi-Dirac distribution, it is sufficient to measure the spectra within the width of 400 mev. The difference of energy resolution is estimated at most 0.2 mev against the spectrum width of 400 mev, much less than the energy resolution of a few mev shown above, and negligible for fitting the measured spectrum to the Fermi-Dirac distribution function. It is also found from the results of Tables 2-5 that the energy resolution would be much better in a case of measurement of electrons for the emission angle restricted within ±0.4. The energy resolution can be suppressed less than 0.02 % with respect to the retarding energy. Moreover the kinetic energy reaches no threshold energy. If the whole assembly of electrodes with many axes of apertures in Fig. 1 has a sufficient counting rate to build up the highly sensitive spectrum, the restriction of the emission angle will be a good option with no additional measurement techniques. 4. Conclusion Electron trajectories were simulated to investigate the capability of the newly designed retarding type electron energy analyzer implementing an electrostatic lens system. The energy resolution of the analyzer was found to depend linearly on the retarding energy and to be 0.05 % against the retarding energy. The voltages to be applied to the electrodes in the analyzer were found to be controllable linearly against the retarding voltage. It is also found that the analyzer has threshold energies whose effect to the energy resolution can be excluded with a combination of a lock-in amplifier and an auxiliary grid. The present

5 242 SICE JCMSI, Vol. 6, No. 4, July 2013 estimation for the newly designed electron analyzer by trajectory simulation promised a sufficiently high energy resolution to construct a practicable photoelectron thermometer for thermodynamic temperature measurement of solid surfaces. References [1] R.I. Masel: Principles of Adsorption and Reaction on Solid Surfaces, Wiley, [2] T.A. Jung, R.R. Schlittler, and J.K. Gimzewski: Conformational identification of individual adsorbed molecules with the STM, Nature, Vol. 386, pp , [3] G.P. Lopinski, D.J. Moffatt, D.D.M. Wayner, and R.A. Wolkow: Determination of the absolute chirality of individual adsorbed molecules using the scanning tunneling microscope, Nature, Vol. 392, pp , [4] S. Hüfner: Photoelectron Spectroscopy, 2nd edn, Springer- Verlag, [5] I. Kinoshita and J. Ishii: Photoelectron thermometry as a novel method to measure thermodynamic temperature, Int. J. Thermophys., Vol. 32, No. 7 8, pp , [6] J.T. Yates: Experimental Innovation in Surface Science, Springer-Verlag, [7] E. Harting and F.H. Read: Electrostatic Lenses, Elsevier, [8] D.A. Dahl: SIMION for the personal computer in reflection, Int. J. Mass Spectrom., Vol. 200, No. 1 3, pp. 3 25, Ikuo KINOSHITA He received his Ph.D. degree from Science University of Tokyo, Japan, in In 1995, he joined the faculty of Yokohama City University, where he is currently an Associate Professor of the Department of Nanosystem Science. His research interests include photoelectron spectroscopy in surface science. He is a member of JPS. Juntaro ISHII (Member) He received his Ph.D. degree in Physics from Keio University, Japan in He joined National Research Laboratory of Metrology (NRLM) in 1996 and started his research on radiation thermometry and its standards. In 2002 he worked for infrared radiation measurements at National Physical Laboratory in UK as a guest researcher. He is currently a head of radiation thermometry section of National Metrology Institute of Japan (NMIJ), AIST. His research interests include temperature measurements and its standards.